The present invention relates generally to digital filter systems and more specifically to adaptive recursive filters.
An adaptive signal processing system is a system that is capable of altering or adjusting its parameters in such a way that its behavior, through contact with its environment, changes to approximate a desired response. A common application is in the field of telephony where problems in acoustic echo cancellation, line echo cancellation and the like readily lend themselves to solutions based on adaptive signal processing techniques. Other fields of use include mechanical systems, radar, sonar, and biological systems.
A commonly used architecture for implementing adaptive systems is the finite impulse response (FIR) filter. The algorithm commonly used for training this type of filter involves adjustment of the parameters based on the error and the derivative of the output with the parameters. This algorithm up until this point has not been available for the training of IIR filters due to the inability to determine the value of the derivatives. The following is a listing of the techniques used to overcome this deficiency in the training of IIR filters.
For example, U.S. Pat. No. 5,638,439 relates to echo cancellation in a transmission line and teaches a method of updating filter coefficients by taking the absolute values of the coefficients and scaling the resulting vector.
U.S. Pat. No. 5,418,849 is directed to a procedure for adapting a recursive filter using an algorithm based on a variation of Kalman""s algorithm. The ""849 patent modifies the Kalman algorithm by taking the decimation of the square error rather than the voice signal to achieve improved speed of convergence. U.S. Pat. No. 5,337,366 discloses in FIG. 1 a filter (16) comprising a non-recursive portion (18) and a recursive portion (17). Coefficient control stages (19-21) serve to update the filter coefficients. The ""366 patent shows the use of finite impulse response (FIR) filter stages (31,32) to filter the signals prior to handling by the coefficient control stages.
U.S. Pat. No. 5,335,020 describes a ghost canceling application used in video systems. The patent addresses the inherent instability of adapting IIR filters by providing for a step of determining the onset of such instabilities. The determination is accomplished by summing the weighting coefficients; if the sum exceeds 1 then the filter may be unstable, and appropriate action can be taken.
U.S. Pat. No. 5,226,057 discloses a digital notch filter implemented using an adaptive IIR filter. The filter coefficients are updated in accordance with equations disclosed beginning at column 2, line 62 of the reference.
U.S. Pat. No. 4,751,663 is directed to an IIR filter wherein a polynomial multiplies both the denominator and the numerator of the system transfer function to remove a zxe2x88x921 term in the denominator. This permits high speed operation with a pipeline processing technique.
The present invention is a method of adapting a recursively defined control processing system that includes obtaining derivative terms of the output with respect to each of the filter coefficients which define a recursive filter. These derivative terms are combined with an error signal in a computation of the update values for the filter coefficients. Subsequent to one such cycle of updating the coefficients, resulting transients in the filter are allowed to settle prior to repeating a next cycle of updating.
In a preferred embodiment, the error signal is sampled over a period of time so that a set of error samples is collected. The derivatives are obtained by use of derivative functions which are functions whose level is representative of the derivative of the filter""s output with respect to the recursive parameters in question. By obtaining and using the derivatives of the output with respect to all parameters, the technique common to the training of FIR filters can be used. Since the technique for the development of these derivative functions is recursive, some restrictions must be placed on how often the parameters can be updated, and that sufficient time is allowed to pass after an update before new update data is collected.
The technique just discussed for adjustment of the recursive parameters places no restriction on the use of non-recursive parameters, and so it is a natural process to combine the techniques used for adjustment of both parameters into one overall system. The discussion in this application will center around a sampled system and the use of z-transforms, but the techniques discussed should not be considered restricted to them.
Further in accordance with the present invention, a control processing apparatus comprises means for receiving an input signal, means for filtering the input signal to produce an output signal, means for producing an error signal, and means for updating the parameters which characterize the filtering means. In accordance with the invention, the filter parameters implement a recursive element; and in an alternate embodiment of the invention, the filtering means further includes a non-recursive element. The updating means includes a derivative function generator for obtaining derivative terms of the output signal with respect to the filter parameters. The derivative terms are combined with the error terms to produce adjustment values to be subsequently combined with the parameters. The filter further includes a delay means for providing a delay period before the updating means proceeds with its next iteration.